calculus – if \$u = arccos (frac{x+y}{sqrt{x}+sqrt{y}})\$ then \$xfrac{partial u}{partial x} + yfrac{partial u}{partial y}\$

Edit: this is a repost
Context: i’ve looked at PYQ’s and this year mock tests and found out that this question was one of the most repeated ones and i’m having an exam next week and my teachers are not available

$$xfrac{partial u}{partial x} + yfrac{partial u}{partial y} = frac{-x(sqrt{x}+sqrt{y}-(x+y)frac{1}{2sqrt{x}})} {sin^2(u)(sqrt{x}+sqrt{y})^2}- frac{y(sqrt{x}+sqrt{y}-(x+y)frac{1}{2sqrt{y}}) } {sin^2(u)(sqrt{x}+sqrt{y})^2}$$
1.$$frac{-1}{2}sin(u)$$
2. $$frac{-1}{2}cot(u)$$
3. $$frac{-1}{2}tan(u)$$
4. $$frac{-1}{2}cos(u)$$